In cases when the bride and groom are issuing the invitation to a wedding, the names of both sets of parents are simply not included on the invitation.
The reason that they are there in traditional invitations is twofold: for Christian weddings, the bride's parents are traditionally the hosts of the wedding, a custom which comes from the old tradition of giving their daughter into the care of her husband. In the Jewish tradition, both the parents of the bride and the parents of the groom are included in the invitation as they each take part in the ceremony.
If you feel very strongly that both your parents and the groom's parents should be included on the invitation, then I would suggest that you go with a derivative of the traditional Jewish invitation wording.
This issue comes up a lot, as it is often assumed that the people listed on the invitation are the ones who are paying for the wedding. This is not necessarily true.
The bride's parents or parent, usually issue the wedding invitations. (The exception is Jewish weddings, for which both the bride's and groom's parents issue the invitation.) In the Christian tradition, the groom's parents are not included on the wedding invitation. If the bride and groom issue the invitation themselves, it is generally assumed by the guests that the parents are not hosting the event.
The items in parenthesis are optional, depending upon your situation. If your wedding is to take place in a house of worship, the second line should read "honor of your presence" or "honor of your presence." (Both are correct; just remember to carry the British spelling throughout the invitation suite if you choose "honor," i.e. "The favor of a reply...".) If the ceremony is to be held outside a house of worship, then "pleasure of your company" is the correct wording.
For the time line, if your wedding is at a time which may be confusing (9 o'clock, for example, could either be a morning or an evening wedding), then you may add the time and day of designation.
If there is more than one location in the city in which you are to be married with the same name (two churches with similar names, like St. Anthony and St. Anthony of Padua, or two Orchard Country Clubs, for example), then it is important to provide a street address to eliminate the possibility of guests arriving at the wrong location.
There's a common misconception that the people listed on the wedding invitation are the ones paying for the event. However, according to etiquette the bride's parents, if they are alive, always issue the invitation to the wedding. That said, if you and your fiance issue the invitation yourselves, it will probably be assumed by your guests that you are paying for the wedding.
If you feel very strongly that your parents should be listed as the hosts of the reception, then that information, again, according to strict etiquette, should appear on a separate reception card.
Since your wording is far from traditional, following the strict etiquette prescribed for wedding invitations seems rather pointless, however. Given the less formal tone that you've chosen, the wording you have indicated seems perfectly fine.